Question

What’s the given m ABC = 70 and m ADC = 46

Answer 1

Answer:

Step-by-step explanation:

Properties of a kite;

1). A kite has one pair of equal angles.

2). A kite has two pairs of adjacent sides.

3). Diagonals of a kite intersect at 90°.

4). Kite has at least one diagonal that bisects the opposite angles.

It's given in the question,

m∠ABC = 70° and m∠ADC = 46°

By the property number -4,

m∠2 = m∠3 = $\frac{70}{2}$ = 35°

m∠8 = m∠9 = $\frac{46}{2}$ = 23°

By the property number - 3,

m∠4 = 90°

By the property of interior angles in a triangle,

m∠3 + m∠4 + m∠5 = 180°

35° + 90° + m∠5 = 180°

125° + m∠5 = 180°

m∠5 = 55°

Similarly, m∠1 + m∠2 + 90° = 180°

m∠1 + 35° + 90° = 180°

m∠1 = 55°

Now m∠6 + 90° + m∠8 = 180°

m∠6 + 90° + 23° = 180°

m∠6 = 180 - 113 = 67°

Therefore, m∠6 = m∠7 = 67°

Answer 2

The values of all 9 angles shown were found using the property of a kite they are:

∠1=55°

∠2=35°

∠3=35°

∠4=90°

∠5=55°

∠6=67°

∠7=67°

∠8=23°

∠9=23°

What are the characteristics of a kite?

One pair of equal angles, two pairs of equal adjacent sides, diagonals intersect at a right angle.

∠1=∠6 because AB=AC

∠6=∠7 because AD=DC

∠2=∠3 because triangle ABC is a combination of two congruent triangles.

∠8=∠9 because triangle DAC is a combination of two congruent triangles.

∠4=90°diagonals intersecting at the right angle.

It is given that

∠2+∠3 = 70°

Since they are equal so ∠2=∠3=35

∠8+∠9 = 46°

Since they are equal so ∠8=∠9=23°

∠5 = 180-∠3-∠4 = 180-35-90=55°

Similarly, ∠1 = 55°

∠6+∠7 = 180-∠8-∠9 = 180-46 = 134°

Since they are equal

∠6=∠7 = 67°

Therefore, all 9 angles were calculated using property of a kite.

∠1=55°

∠2=35°

∠3=35°

∠4=90°

∠5=55°

∠6=67°

∠7=67°

∠8=23°

∠9=23°

To get more about kites refer to:

https://brainly.com/question/16424656